In many digital modulation schemes, binary data is mapped onto modulation symbols. In many such schemes, there are more than two possible different modulation symbols, which means each modulated symbol contains more than 1 bit of information. Symbols received at a receiver may be corrupted by noise. Thus, due to the randomness characteristic of noise, a recovered sequence of bits from received symbols could have errors in it. In other words, each recovered bit is not guaranteed to be the original transmitted bit. Some of the recovered bits are more likely to be wrong than others. Soft bits, also referred to as reliability information, are used to indicate the probability of each recovered bit to be in error. This “soft information” is especially useful for an error control decoder.
Typical digital modulation schemes calculate the soft bits through a series of computationally intensive equations. For example, in a constellation having 8 symbols, such as in the 8-PSK modulation scheme, each symbol represents three bits of data. In order to calculate soft bits, a distance between the received symbol and each symbol in the constellation, as well as the minimum values of 6 groups of distance values are calculated. In particular, the six groups of distance values are the groups having a 0 or 1 in the first bit, a 0 or 1 in the second bit, and a 0 or 1 in the third bit. For example, given the exemplary constellation 100 in FIG. 1, the soft bits are calculated using the three equations below:z3i=min(Mi1,Mi2,Mi3,Mi4)−min(Mi0,Mi5,Mi6,Mi7));z3i+1=min(Mi3,Mi4,Mi5,Mi6)−min(mi0,Mi1,Mi2,Mi7));z3i+2=min(mi2,Mi3,Mi7,Mi8)−min(mi0,Mi1,Mi4,Mi5))
In the above equations, the quantity Mij represents the distance between the received symbol and one of the symbols in the constellation. The subscript i is the received symbol index and the subscript j is the constellation symbol index. Performing these calculation for each received symbol can be computationally intensive because the calculations involve complex numbers and square roots. In addition, other constellations that map more than 3 bits to each symbol will have additional equations to be solved, one for each soft bit.